[HN Gopher] The Infinity Machine
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The Infinity Machine
Author : Smaug123
Score : 61 points
Date : 2024-07-25 19:50 UTC (5 days ago)
(HTM) web link (www.chiark.greenend.org.uk)
(TXT) w3m dump (www.chiark.greenend.org.uk)
| Demonoculus wrote:
| While I am not an expert, but won't it run into Xeno's like
| paradox? But makes for interesting reading.
| teraflop wrote:
| What do you mean by "run into"?
|
| Zeno's paradoxes are thought experiments. The original paradox
| of Achilles and the tortoise purported to show that Achilles
| would never be able to overtake the tortoise. But of course, in
| a real race Achilles would encounter no difficulty whatsoever
| in doing that.
|
| The Infinity Machine almost certainly isn't physically
| possible, but that's because of the laws of physics, not
| because of Zeno.
| astrodust wrote:
| Unless there's an infinite number of programs of finite size,
| which sounds impossible, then no.
| Schiphol wrote:
| There's work on so-called "hypercomputation" that might relevant
| to the author's project:
| https://en.wikipedia.org/wiki/Hypercomputation
| ryankrage77 wrote:
| Also see Supertasks, https://en.wikipedia.org/wiki/Supertask
| its_ethan wrote:
| VSauce is a little silly, but genuinely does have great
| content packed in his videos, and he has one on Supertasks:
| https://youtu.be/ffUnNaQTfZE
| jackofspades wrote:
| This just came up on a separate recent HN thread... the
| fictional hypercomputer: "I Don't Know, Timmy, Being God Is a
| Big Responsibility" by qntm: https://qntm.org/responsibility
| tlocke wrote:
| I know the light switch idea as Thomson's lamp:
|
| https://en.m.wikipedia.org/wiki/Thomson%27s_lamp
|
| I used it as an interview question many years ago. I wasn't very
| rigorous about it, basically any plausible answer was good enough
| for me. Answers fell into two categories, the theorists (it's an
| infinite series that doesn't converge) and the pragmatists (you
| couldn't physically do it).
| taneq wrote:
| As anyone who's played light switch disco will know, the light
| bulb will blow long before you reach the theoretical limit of
| the series. :D
|
| (Actually thinking about it, that's probably not true because
| the switching accelerates so fast... the limiting factor is
| probably actually friction from moving the switch, and/or the
| tensile strength of the switch housing. I wonder if it would
| just disintegrate or if it would build up enough heat to
| properly explode...?)
| mitthrowaway2 wrote:
| I think the limiting factor will be the inductance of the
| wire and lightbulb filament, which sustains a current even
| when the switch attempts to break the circuit!
| pixl97 wrote:
| You'll have to get a planck switch and a single electron
| bulb... problem is it may or may not exist at any given
| moment, especially where you want it.
| jerf wrote:
| I'll give you a good in between. The problem is underspecified
| because the universe in question is underspecified. You can get
| pretty much any result you want out of such a strange thing by
| specifying a more fully-fleshed out universe in which that is
| the answer. You can create one in which the answer is half-on,
| half-off, even though you initially specified your cells as
| only containing integers and not realized that your axioms
| entailed additional values, which themselves could be limited
| to rationals with the right axioms, or the computables, or the
| reals, or several other things.
|
| In this, your universe may admit of a natural "averaging"
| operation, where you take a "half on" thing and a "quarter on
| thing" and produce a "three quarters on thing" in some natural
| manner. Playing around in my head, I find you need to be
| careful about your definition of "fully on" and "fully off"
| here; you may or may not want to permit an "infinite sequence"
| that contains zero changes in it. But you'll get a weirder
| number system if full-on and full-off are not permitted, where
| you can arbitrarily close to them but not quite achieve them.
|
| Or you may find your axioms force you to admit a new
| "undefined" value that, again, you didn't realize when you
| started that you were adding but it turns out you were. Or you
| could create a scenario where this actually freezes your entire
| universe because there simply is no way to proceed past the
| singularity, because your "take next step" function simply
| stops working and you get the mathematical equivalent of a
| crashed or hung program. (Just because something is
| "mathematical" does not imply totality; there's many, many,
| many cases where the answer is just "That function doesn't work
| there". Sometimes that leads to an exploration of "well what if
| we force it anyhow", e.g., "square root of negative numbers",
| but sometimes it really is just "this function stops here".)
|
| An intriguing exercise for those who may want to experience
| this sort of "I didn't realize these axioms did that!" first
| hand is to look up the "surreal numbers" if you've never heard
| of them before. Read the definition of surreal and try to guess
| what numbers will emerge from it. Then watch as your mind is
| blown about what you admit when you admit those axioms.
| Unfortunately, I could not find a presentation of surreal
| numbers that started with the bare definition; for obvious
| reasons everyone leads with where you're going because who
| reads unmotivated mathematical definitions for fun, right?
| Still, try to imagine what you would have _expected_ such
| axioms to produce, what someone might have "intended" them to
| produce, versus what the actually do.
| nom wrote:
| > .. they say that its sum is 1/2. And this answer does not
| help us, since we attach no sense here to saying that the lamp
| is half-on.
|
| Maybe a lamp is a bad example, it is clearly half-on: PWM
| modulated with 50% duty cycle and infinite frequency. I don't
| see any Problem ;)
| pixl97 wrote:
| Darn quantum lamps
| mistermann wrote:
| With the plunging cost/capability of AI compute, variations of
| this are becoming more plausible every day. Who will be the first
| mover?
| its_ethan wrote:
| Even with plunging cost and increasing capability... this is
| talking about _infinite_ compute, it 's essentially impossible
| to achieve by definition.
|
| You could dedicate the worlds entire compute to the Goldbach's
| conjecture function he wrote up - it (would/might) _never_
| complete. You could 1000000x the worlds compute and it (would
| /might) _never_ complete. It 's not even a problem of compute
| speed, it's a problem with infinity.
| mistermann wrote:
| Agreed, but there is plenty of utility that can be harvested,
| if we can direct our attention adequately.
|
| Also: humans have the ability to arbitrarily redefine words,
| _and believe those redefinitions_! There is a surprising
| amount of leeway in this simulation.
| ben_w wrote:
| > Agreed, but there is plenty of utility that can be
| harvested, if we can direct our attention adequately.
|
| Only for problems no worse than O(n^m) where m is not much
| more than 1.
|
| Greenend (the domain name in the link) is, or so goes local
| legend, named after an actual street in Cambridge, quite
| close to where I was working a decade ago; one particular
| job, we'd just changed a file format for a mobile app, and
| the upgrade process was taking 20 minutes on test devices.
| The other engineer insisted it couldn't possibly be
| improved despite the two observations (1) it was fine
| before the upgrade, and (2) it was fine once the upgrade
| was complete. After a bit of digging, I found an O(n^2)
| operation we didn't need, and turned 20 minutes into 200
| ms.
|
| Increase the available compute by a factor of 1024 in an
| O(n^2) task, only compensates for n growing by a factor of
| 32.
| VikingCoder wrote:
| I'm once again reminded of the book Permutation City...
| nickcw wrote:
| Yes, I was thinking this would make a good basis for a Greg
| Egan story too.
| cvoss wrote:
| If such a machine existed in our universe, as it sped up its
| execution, its parts would approach the speed of light. To
| continue speeding up its execution, it necessarily must occupy a
| smaller and smaller volume, to keep the parts nearer and nearer
| to each other. Continue further, and you realize that the total
| information content of the machine can't be sustained at any
| amount without the thing collapsing itself into a black hole. So,
| even if the machine, in any sense, "finishes" the computation,
| the output will live inside a black hole and thus be physically
| unknowable to us.
|
| I find it so fascinating that fundamental properties about the
| laws of physics integrate so tightly with what is computable. The
| standard definition of compatibility involving Turing machines
| sounds kind of arbitrary, but those machines are representative a
| truly fundamental concept in our universe: that which is
| physically knowable, since you can build Turing machines out of
| the stuff in the universe.
|
| Almost. Turing machines have unbounded tape. But the universe
| does not contain an unbounded amount of information or space with
| which to work. Sufficiently large Turing computations, though
| theoretically finite, are not realizable in our universe. Should
| such computations be considered decidable or undecidable?
| sqeaky wrote:
| I am not sure if such is decidable or not, but your conjecture
| is decidedly against the spirit of the post. :p
| waveBidder wrote:
| You would probably enjoy Feynman's lectures on computation:
| https://www.goodreads.com/book/show/17274.Feynman_Lectures_O...
| Quekid5 wrote:
| > Sufficiently large Turing computations, though theoretically
| finite, are not realizable in our universe. Should such
| computations be considered decidable or undecidable?
|
| In Practice, I think Undecidable is the only "correct" answer
| -- because our knowledge is still very incomplete. In
| Theory/Principle I think Decidable is the "correct" answer
| because there will _very probably_ be limits that cannot be
| exceeded.
|
| ... but then, to reduce this to a simpler issue: The Halting
| Problem becomes trivial for any amount of finite state. It just
| takes a really, really long time (or a huge amount of space) to
| decide.
| omoikane wrote:
| I thought it's interesting that the author went the way of add-
| more-via-subdivision. It feels very analog, kind of like how with
| old photos, the way you get more resolution is to just print them
| bigger (of course, what you actually get in reality is more
| grain).
|
| It's different from how we modeled things like Turing machines,
| where if we needed more memory, we would append more tape, as
| opposed to subdivide the existing tape further.
| rahimnathwani wrote:
| Tangential:
|
| 1. Simon Tatham is the author of PuTTY
|
| 2. In the early days of the web, many people's personal sites
| were hosted on shared computers (e.g. my first was on my
| university's DEC Ultrix system). The URLs started with a
| reference to the user's home directory. This page is hosted on a
| machine that has a page to lists all the user's home pages:
| https://www.chiark.greenend.org.uk/users.html
|
| 3. The home page has this awesome spam detector:
| If you want not to be able to send mail here in future, please
| send mail to tabasco@chiark.greenend.org.uk.
| vermilingua wrote:
| 2a. The machine name (chiark) is a reference to The Player of
| Games, a fantastic book in the excellent Culture series by Iain
| M. Banks
| ben_w wrote:
| 4. Domain created: 1985-07-24
|
| It predates the web by about 4 years, the publication of the
| first HTML standard by about 6 years, and it just had its
| 39th birthday.
| sqeaky wrote:
| Such a machine would be fun
|
| I would make a programming language where you couldn't write
| code, only detailed specifications and tests. In a VM Every
| possible permutation of bytes/opcodes/instructions/whatevers
| would be tests to produce the smallest and fastest (presuming the
| code is to run on other machines) possible binaries that pass
| your tests. Ideally this would produce a Pareto front of possible
| outputs and you could choose from among them.
|
| Another idea solving old problems the hard way. Since fermat's
| last theorom is countably infinitely problem and this computer is
| uncountably infinite in performance it should be able to knock it
| instantly by simply enumerating all integers and trying them.
| sqeaky wrote:
| If we used such a machine to to enumerate Pi what would happen?
| Is it proven that Pi infinitely long? If so that would be a
| countable infinite because it is digits of precision, right?
|
| Could we write algorithms that search all the digits of pi for
| patterns? Or mayb messages on speculation of creators or others
| who might be able to tamper with it?
|
| Could other math things be searched? Have we proven there is no
| upper limit to prime numbers? I know the largest known mersenne
| prime fills a novel sized book with just one number, but when
| does a number get too big to be prime if ever?
| TwentyPosts wrote:
| Yes, pi has an infinitely long decimal expansion, and there are
| infinitely many prime numbers.
|
| No deep messages have been found in either yet, and I am sure
| some people tried, so it stands to reason that no such messages
| exist. Mathematical objects can be complicated and difficult to
| understand and go on for infinitely long without having secret
| messages hidden in them.
| sqeaky wrote:
| Of course they can, and with an infinitely powerful machine
| it would be cheap to check.
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